An efficient iterative algorithm for common solutions of three G-nonexpansive mappings in Banach spaces involving a graph with applications to signal and image restoration problems

Abstract

In this paper, three G-nonexpansive mappings are implemented and analyzed using an efficient modified three-step iteration algorithm. Assuming coordinate-convexity in a uniformly convex Banach space endowed with a directed graph, conditions for the weak and strong convergence of the scheme are determined. We give numerical comparisons to back up our main theorem, and compare our algorithm's convergence behavior to that of the three-step Noor iteration and SP-iteration. We use our proposed algorithm to solve image deblurring problems as an application. In addition, we discuss a novel approach to signal recovery in situations where the type of noise is unknown.

Keywords

• coordinate-convex
• g-nonexpansive mapping
• weak and strong convergence
• signal recovering problem
• image deblurring problem